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We present a model in which fire sales propagate shocks across bank balance sheets. When a bank experiences a negative shock to its equity, a natural way to return to target leverage is to sell assets. If potential buyers are limited, then asset sales depress prices, in which case one bank's sales impact other banks with common exposures. We show how this contagion effect adds up across the banking sector, and how it can be estimated empirically using balance sheet data. We compute bank exposures to system-wide deleveraging, as well as the spillovers induced by individual banks. Applying the model to European banks, we evaluate a variety of interventions to reduce their vulnerability to fire sales during the sovereign debt crisis.